Tunneling phenomenon

D. V. Averim and K. K. Likharev developed a theory for describing the behavior of small tunneling junctions based on electron interactions. They had started from previous work on Josephson junctions (Likharev and Zorin 1985, Ben-Jacob 1985, Averin and Likharev 1986b) and established the fundamental features of the single-charging phenomena. Their work is based on a quantization theory and handles the tunneling phenomenon as a perturbation, described by annihilation and creation operators of a Hamiltonian. 

Fig. 9 Schematic of the inelastic electron tunneling phenomenon. From M. Galperin et al. Science (2008), 319, 1056-1060. Reprinted with permission from AAAS...

These studies had therefore found the tunneling phenomenon, with coupled motion, as the explanation for failures of these systems to conform to the expectations that the kinetic secondary isotope effects would be bounded by unity and the equilibrium effect and that the primary and secondary effects would obey the Rule of the Geometric Mean (Chart 3), as well as being consistent with the unusual temperature dependences for isotope effects that were predicted by Bell for cases involving tunneling. 

Field emission is a tunneling phenomenon in solids and is quantitatively explained by quantum mechanics. Also, field emission is often used as an auxiliary technique in STM experiments (see Part II). Furthermore, field-emission spectroscopy, as a vacuum-tunneling spectroscopy method (Plummer et al., 1975a), provides information about the electronic states of the tunneling tip. Details will be discussed in Chapter 4. For an understanding of the field-emission phenomenon, the article of Good and Muller (1956) in Handhuch der Physik is still useful. The following is a simplified analysis of the field-emission phenomenon based on a semiclassical method, or the Wentzel-Kramers-Brillouin (WKB) approximation (see Landau and Lifshitz, 1977). 

The surface states observed by field-emission spectroscopy have a direct relation to the process in STM. As we have discussed in the Introduction, field emission is a tunneling phenomenon. The Bardeen theory of tunneling (1960) is also applicable (Penn and Plummer, 1974). Because the outgoing wave is a structureless plane wave, as a direct consequence of the Bardeen theory, the tunneling current is proportional to the density of states near the emitter surface. The observed enhancement factor on W(IOO), W(110), and Mo(IOO) over the free-electron Fermi-gas behavior implies that at those surfaces, near the Fermi level, the LDOS at the surface is dominated by surface states. In other words, most of the surface densities of states are from the surface states rather than from the bulk wavefunctions. This point is further verified by photoemission experiments and first-principles calculations of the electronic structure of these surfaces. 

Chen, C. J. (1991c). Attractive atomic force as a tunneling phenomenon. J. Phys. Cond. Matter 3, 1227-1245. 

A compound ion may dissociate in a high applied electric field into a neutral atom and an ion. This dissociation process, generally known as field dissociation, was theoretically treated by Hiskes123 in 1961 as an atomic tunneling phenomenon. It is similar to field ionization of an atom... 

Inner-sphere reactions also use the tunneling phenomenon, but in this case a single ligand is the conduit. The reactions proceed in three steps (1) a substitution reaction that leaves the oxidant and reductant linked by the bridging ligand, (2) the actual transfer of the electron (frequently accompanied by transfer of the ligand), and (3) separation of the products ... 

Inner-sphere reactions use the tunneling phenomenon with a ligand as the conduit. These reactions proceed in three steps (1) a substitution reaction that leaves the oxidant... 

In chemistry, there are a great number of processes where the tunneling phenomenon is important. It may be necessary to nse a more accurate treatment than the standard tunneling model, however. 

In most cases, molecular dynamics is less useful at a lower temperature. Low energy quantum states are involved, where classical mechanics is less successful. At low temperature, the nuclear tunneling phenomenon is more important, relative to the classical motion. Tunneling is not easily taken into account in classical simulations. 

The partially deuterated complex calix-[(H2)2(D2)]TMPA Cu(I) complex gives access to intramolecular kinetic isotope effect values (KIE = 21 at room temperature, up to 29 at 277 K), activation enthalpies and pre-exponential factors in agreement with a tunneling phenomenon, also observed in natural systems. This first oxidation sufficiently lowers the electron density at Cu(I) to prevent further O2 activation. 

The Zhu Nakamma theory also covers other cases such as low-energy collision dynamics, where the incident energy is much lower than the barrier of the lower adiabatic potential (see Ref. [512] for the explicit form appropriate for this parameter range). That is, it can handle correctly and conveniently a system in which nonadiabatic dynamics couples with tunnelling phenomenon. 

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